# Determination of Several Thermodynamic Quantities

```Chemistry 212 Lab
Fall 2004
Simultaneous Determination of Several Thermodynamic
Quantities: K, G&deg;, H&deg;, and S&deg;
Purpose
Study a system of a sparingly soluble salt in water. From the solubility information at various
temperatures, a variety of other thermodynamic quantities can be determined for the system. Among these
thermodynamic quantities are the changes in standard enthalpy, standard entropy, and standard free energy.
Introduction
The system you will be studying involves a relatively simple solubility equilibrium of borax
(Na2B4O7•10H2O) in water:
Na2B4O7 • 10H2O(s) &lt;--=======--&gt; 2Na(aq) + B4O5(OH)42(aq) + 8H2O(l)
Note that the reaction equation, as it is written above, has a few features you should notice:
1). It is written as an equilibrium process
2). 8 water molecules from the hydrated salt are lost to the reaction medium
When defining an equilibrium constant expression for this reaction, the &quot;waters of hydration&quot;, written as a
reaction product above, must now be represented in any expression for the equilibrium constant for this
process. Thus, the proper equilibrium expression for the reaction above has this form:
[Na]2 [B4O5(OH)42] [H2O]8
K = -------------------------------------[Na2B4O7 • 10H2O]
The experimental procedure will specifically state that you are to make sure there is always some solid
borax remaining in the sample mixture before you remove some of it to analyze. That being the case, the
'concentration' of solid borax can be assumed constant, and the equilibrium expression can be simplified:
K = [Na]2 [B4O5(OH)42] [H2O]8
The water term in the expression (which was originally part of borax's crystalline matrix) is lost to the
sample mixture. This added amount of water does not significantly change the concentration of water
already present. The water term can also be 'simplified out' of the equilibrium expression:
K = [Na]2 [B4O5(OH)42]
What remains is now a solubility product constant (Ksp) expression for borax in water. To determine a
value for the solubility product, a method must be found to assay either the amount of sodium ion, or borate
ion, in the sample mixture. The original equilibrium expression, and balanced solubility equilibrium
reaction, leads to a convenient way to express either ion in terms of the other, so that it is possible to define
Ksp in terms of either the concentration of sodium ion, or concentration of borate ion. A series of
substitutions, based on the original balanced solubility equilibrium equation, gives the desired K sp,
expression defined in terms of the borate ion only:
[Na] = 2 [B4O5(OH)42]
K = [ (2 [B4O5(OH)42] ) ]2 [B4O5(OH)42]
Ksp = 4 [B4O5(OH)42]3
Finding the concentration of borate ion, in any sample at any given temperature, leads directly to a value for
solubility product (Ksp) at that temperature.
Design of the Experiment and Relevant Background
For a series of borax-containing samples taken at various temperatures, the concentration of borate
ion will be determined. The borate ion reacts with monoprotic acid (such as HCl) in a 1:2 fashion:
B4O5(OH)42(aq) + 2HCl(aq) + 3H2O(l) ----------&gt; 4 B(OH)3(aq) + 2 Cl (aq)
The amount of HCl consumed (in L) multiplied by the molarity of the acid gives moles HCl. It is a trivial
exercise to determine moles borate ion from there, and dividing by the volume of borate ion-containing
sample in liters gives concentration of borate ion. This general procedure is repeated for borate ioncontaining samples of constant volume obtained at various temperatures.
Calculation of these temperature-dependent values for Ksp of borate ion is but the first step in a
greater sequence of obtaining complete thermodynamic parameters for the dissolution of borax in water.
There are several other important thermodynamic parameters that can be found: free energy change,
enthalpy, and entropy, upon further treatment of the equilibrium constant/temperature base data set. The
next goal will be to estimate the free energy change for this solubility equilibrium. The following equation
immediately shows the relationship between free energy change (G) and equilibrium constant (K):
G = RT ln Ksp
(A)
A value for the equilibrium constant at a given temperature gives (after a sense) the value for free energy
change directly. The free energy change at a given temperature is itself related to both the change in
enthalpy, and the change in entropy, by the following equation:
G = H  TS
Combining the two equations relates K, H, and S in a single statement:
RT ln Ksp = = H  TS
(B)
The preceding equation can be rearranged into a form that is linear. When re-arranged into a linear form,
1/T and ln Ksp can be used as (x,y) points on a graph. The slope of such a graph is related to the change in
enthalpy and the change in entropy is related to the y-intercept:
ln K sp =
ln K sp =
y
=
-H
+
RT
TS
RT
S
-H
1
R
T
R
m
x +
b
+
A summary of the post-data collection activities reveals the true beauty of this experiment. Once the
solubility product constants have been determined for 5 different temperatures,
• A table of free energy values (G) with the temperatures those values correspond to should be compiled.
This is most conveniently done using equation (A), with values for Ksp and the temperatures for which they
are valid.
• A graph of ln Ksp vs. 1/T should be made, the slope of which is related to change in enthalpy.
• The same graph has a relationship between change in entropy and its y-intercept
The experiment requires that the solubility of borax be found at various temperature values. Samples of
saturated borax solution are collected at no less than 5 different temperatures, four above room temperature,
and one close to or at room temperature. These samples are then warmed (if necessary) to re-dissolve any
precipitated borax, and titrated to the yellow bromocresol green endpoint with standardized aqueous
hydrochloric acid.
Experimental Procedure (groups of 2 students)
Note: to complete this procedure, it will be necessary to carefully divide the tasks between partners. Take a moment before
beginning to make a plan between the two of you to do this.
Using a 5 mL pipet, add exactly 5 mL of distilled water to each of ten test tubes. Mark the level with a
grease pencil or other marker and pour the water out. Each group is assigned a temperature at which to do
the titrations. Mark two of the tubes with your assigned temperature. Your data will be pooled with data
from your classmates to arrive at the temperature dependence from room temperature to about 45&deg;C.
Using a hot plate, prepare a mixture of 30-32 g of solid sodium borate decahydrate (i.e. borax) and 150 mL
of distilled water in a 250 mL beaker. Begin heating the mixture, but do not allow the temperature of the
mixture to exceed 50&deg;C. If all of the borax dissolves, add more so that an excess of solid borax exists in the
beaker at 45&deg;C. If there is solid borax in the mixture, you can assume the water is as saturated with
dissolved borax as it can get, and this is the condition you want. Once the mixture has exceeded, however
slightly, the 45&deg;C mark, remove the beaker to the bench top and replace it with a beaker containing 150 mL
of distilled water (this will be used later, but it is best to begin heating it now). This water should also not
be allowed to exceed 50&deg;C.
Taking Samples of the Borax Solution
Continue to stir the borax/water mixture occasionally until it has cooled to the assigned temperature. Then
as quickly as possible, and trying to avoid the transfer of any solid borax, carefully pour out 5 mL of the
solution into the two test tubes marked with your temperature. Be sure to note the actual solution
temperature before and after this transfer, and use the average if the readings differ by more than 1&deg;C.
It will be not be necessary to cool the sample in an ice bath to speed up sampling. Doing so risks
introducing errors due to supercooling, and should be avoided. Experience has shown that a 5-degree
temperature drop can occur in about 10 - 15 minutes, and your patience will be rewarded with excellent
samples from which to obtain data.
Titration of the Borax Samples
The second water bath should have reached at least 45&deg;C. If it has, try your best to keep it at this
temperature. Place the samples in the hot water bath until any re-precipitated borax has dissolved.
Carefully pour the dissolved borax solution into a 125 mL Erlenmeyer flask containing 50-75 mL of
distilled water and 10 drops of bromocresol green indicator. More water may be added to the flask, and the
test tubes can be rinsed with water from the hot water bath, to ensure that all the borax has been transferred
and is in solution before beginning the titration. The borax samples should have a blue color before they are
titrated with acid.
Set up a 50 mL buret and fill it with the standardized HCl solution. You will need to obtain enough HCl
solution, and have it standing by at your bench, to fill the buret twice. Expel the air bubbles from the buret,
take an initial volume reading, and titrate the borax sample until the blue color disappears and the sample
turns yellow. This is the endpoint of a bromocresol green titration. Take a final volume reading and
immediately begin preparing the next sample to be titrated. You may wish to use the final volume of one
titration as the initial volume of the next, and you can--provided more acid has not been added to the buret.
A full buret (50 mL) of acid should be sufficient to titrate the full temperature range of one of the two sets of
samples.
Repeat this titration procedure until at least one set of borax samples, covering the complete temperature
range, has been titrated. If time permits, you should do all ten to get the best possible data set, and to be
able to 'selectively edit' from your data any &quot;bad&quot; samples or mistakes.
The remaining borax mixture, and all titration samples, can be flushed down the drain with running water.
Please carefully rinse your buret before returning it. Allow the hotplate to cool before returning it to the
cabinet.
Data Handling and Analysis
Use the data of initial and final HCl volumes, and molarity of HCl, to calculate number of moles of borax in
each titrated sample.
Calculate values for the solubility product constant (Ksp) for borax at the various temperatures.
Remember to convert your temperature values to Kelvin for purposes of finding thermodynamic quantities.
Plot ln Ksp vs. 1/T for all ten samples. Determine H (kJ/mol) and S (J/mol K) from this graph.
Calculate the values for G for each sample using:
1). Equation (A)
2). Equation (B), with your solved values for H and S as found earlier. Note that you'll assume that H
and S are constant over this temperature range. Are they?
Plot G vs. T for both methods of finding temperature-dependent free energy change values.
Data Tables -- Simultaneous Determination of Several Thermodynamic Quantities
Molarity of Standardized HCl
__________
Room Temperature, &deg;C
__________
Solution Temperature
Room Temperature, K
Trial #1
Trial #2
Volume of Borax Solution
__________
__________
Final Volume, HCl
__________
__________
Initial Volume, HCl
__________
__________
Total Volume, HCl
__________
__________
Moles HCl
__________
__________
Moles Borax
__________
__________
Concentration of Borax in sample
__________
__________
Solubility Product, Ksp
__________
__________
Average Ksp
__________
__________
Free Energy Change, G
__________
__________
Graphically Determined Values
Change in Enthalpy, H
__________
Change in Enthalpy, S
__________
Table of Temperature, Equilibrium Constant, and Free Energy Change Values
Temperature (&deg;C)
40
35
30
25
Room (_____)
Temperature (K)
Free Energy Change (G)
Equilibrium Constant (K)
```